Numerical analysis of visual patterns

Summary form only given, as follows. Similarities are found between spatial pattern analysis and other low-level cooperative image analysis tasks. Visual pattern analysis proceeds analogously via estimation of emergent 2D image frequencies. Unlike shape-from-X or optical flow paradigms, constraints are derived from the responses of multiple oriented spatial frequency channels rather than directly from the image irradiance measurements. By selecting channel filters that are sufficiently concentrated in both space and frequency, highly accurate spatial frequency estimates are computed on a local basis. Two related methods are proposed. In the first, a constrained estimate of the emergent image frequencies is obtained by resolving the responses of multiple channel filters in a process similar to photometric stereo. The second approach formulates the estimation of frequencies as an extremum problem regularized by a smoothing term. An iterative constraint propagation algorithm is developed analogous to those used in variational/relaxational approaches to shape-from-X (shading, texture) and optical flow. Examples illustrate both approaches using synthetic and natural images.